A turbine flow meter can be used to measure the flow rate of a liquid. Flow rate information can be used to derive the volume of the liquid to accomplish a volumetric meter. One example of a turbine flow meter is described in U.S. Pat. No. 5,689,071 (hereinafter the “'071 patent.” In the '071 patent, two turbine rotors are contained within the liquid flow path of a meter housing. The turbine rotors rotate as liquid passes across the rotors. The liquid passes through the first turbine rotor and is directed into the second turbine rotor such that the second turbine rotor rotates in a direction opposite from the first turbine rotor.
Another example of a dual rotor turbine flow meter is described in U.S. Pat. No. 5,831,176 (hereinafter the “'176 patent”). In the '176 patent, a description is provided on how the flow rate of liquid is derived from information concerning the rotation of the turbine rotors. During calibration of the turbine flow meter, a known volumetric flow rate of liquid is placed through the meter. As the liquid flows through the meter, the liquid passes through the rotors causing the rotors to rotate. The rotational frequency of the turbine rotors is measured at various flow rates and frequencies to arrive at a “Strouhal” number for each turbine rotor. The Strouhal number is the frequency of the rotor divided by the volumetric flow rate as follows:   Sr  =      fr    Vf  
The corresponding “Roshko” numbers for each of the Strouhal numbers are determined for each of the turbine rotors by dividing the frequency of the rotor by the viscosity of the liquid, as follows:   Rr  =      fr    v  
The Strouhal and corresponding Roshko numbers are plotted on a Roshko-Strouhal (R-S) curve and/or are stored in an array of finite points with the Strouhal numbers being plotted in one axis or an array, typically in the y-axis, and the corresponding Roshko numbers being stored in another axis or corresponding array, typically the x-axis. An example of a R-S curve is illustrated in FIG. 2.
During operation, when the R-S curve is used to determine a Strouhal number from a calculated Roshko number as discussed below, linear interpolation is used to determine numbers that fall in between the finite points of the R-S curve. However, since the R-S curve is not a linear function, linear interpolation will introduce error.
If the R-S curve could be converted into a perfect equation instead of being stored as finite points such that interpolation was not required for its use, error would not exist as a result of interpolation. However, the R-S curve is a complex curve that cannot be easily described by a linear or complex order equation. Further, some processes involve the manipulation of raw Roshko and Strouhal coordinate points calculated during calibration of a meter to remove extraneous points that would cause linear interpolation to introduce even more error. However, even with such manual manipulation, error will still exist to some degree in the R-S curve.
During operation of the meter, the liquid flow rate passing through the meter can be determined using the Roshko and Strouhal data from the R-S curve. If there is any error in the R-S curve, this error will be propagated to the volumetric flow rate calculation that is made by the meter during operation. The volumetric flow rate of liquid flowing through the turbine meter is determined as follows:
First, the rotational frequencies of the turbine rotor are measured. As discussed in the '071 patent, pick-off coils or other sensing devices, such as Hall-effect sensors for example, are employed in the turbine meter to detect the rotation of the turbine rotors. The detection device detects the movement of each blade on the turbine rotor and can therefore determine the frequency of rotation as is described in the '071 patent. Once the rotation frequencies of the turbine rotors are measured, the Roshko number for each rotor can be determined according the formula for the Roshko number shown above. After the Roshko number is calculated, the corresponding Strouhal number is determined by the R-S curve or equation. The Strouhal number and the frequency of the turbine rotor are then used to determine the volumetric flow rate according to the rearranged Strouhal formula below. The Strouhal numbers of each rotor may be combined to use as the Strouhal number in the equation below:   Vf  =      fr    Sr  
The volumetric flow rate calculation is repeated continuously in periodic time increments so that the volumetric flow rate of liquid flowing through the turbine meter is known at any given time. The volume of the liquid can be derived from the volumetric flow rate using time as is well known.
If the turbine flow meter is used in an application in which the liquid flow is distributed aperiodically and frequently, such as in a fuel dispenser where a customer can constantly change the flow of fuel delivery by engaging and disengaging the fuel nozzle, it is more difficult to accurately measure flow rate and volume. Disruptions in the liquid flow result in disruptions in the rotational frequency of the turbine rotors, which in turn affect the calculation of the Roshko numbers. Further, since the R-S curve is derived data that forms a curve where an equation cannot be formulated to perfectly match the curve, approximations of the Strouhal number using the calculated Roshko number will cause error as well. When the R-S curve is determined during calibration, a line is fitted through the raw Strouhal and corresponding Roshko data points, and the process of line fitting introduces error since extraneous points may alter the final R-S curve. The liquid flow rate variations cannot be controlled, but derivation of the R-S curve is a controlled operation. If the accuracy of the R-S curve can be improved to reduce inherent errors present, the accuracy of the volumetric flow rate calculation will also improve.
Therefore, there exists a need to find a technique and method to more accurately approximate data points in an automated fashion where a perfect equation cannot be derived to match the data points and thus finite points of data are used. In the preferred embodiment, the data points are the Strouhal numbers of the R-S curve since error in the Strouhal numbers will cause error in flow rate calculations of a turbine flow meter.